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Interior And Exterior Angles:

A. Interior angles of a regular polygon:

1.  For any polygon, the sum of the interior angles is always:

180 x (n-2), where 'n' is the number of sides

2.  The measure of one interior angle of a regular polygon is determined by the formula:

B.  Exterior angles of a regular polygon:

1.  For all regular polygons, the exterior angle is determined by:

C.  Note: All the above values are specified in terms of degrees.  To convert to radians see Converting To Radians.

D.  Examples

Ex [1]  Each interior angle of a regular n-agon is 120^o.  Then n = ______.

a.  To solve this problem we need to set up an equation using the fact that each interior angle is .

b.  So we know 120 = .  Solving this equation we get 120n = 180n - 360 or 60n = 360.  Solving, we get n = 6.

c.  The answer is 6.

Ex [2]  If the sum of the interior angles of a regular polygon is 1440^o, then the number of sides of the polygon is _____.

a.  Since the sum of the interior angles is 180 (n-2), we can set up the equation 180 (n-2) = 1440.

b.  ¹⁴⁴⁰/₁₈₀ = 8.  So n - 2 = 8, or n = 10.

c.  The answer is 10.

Ex [3]  The exterior angle of a regular octagon is _____ degrees.

a.  Since ³⁶⁰/_n is the formula we use for the exterior angles, we simply divide 360 by 8 which is 45.

b.  The answer is 45.

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